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Timing Pulse Measurement and Detector
Calibration for the OsteoQuant®
Advisor: Dr. Thomas N. Hangartner
By: Binu Enchakalody1
The OsteoQuant®
• pQCT scanner which can provide precise density assessment of the
trabecular and cortical regions of bone.
• Currently being upgraded to a x-ray tube source and a CZT
semiconductor detector.
2Ref: http://www.wright.edu/academics/bmil/bmil1.htm
1. Implement a system capable of registering the motor- and
detector timing-pulses of the Osteoquant® using a common time-
base in microsecond resolution.
2a. Correct the photon-count loss due to dead time to an error level of
less than 0.5% of the maximum expected photon counts.
2b. Correct the non-linearity of the projection values due to beam
hardening to an error level of less than 1% of the expected
maximum projection value.
Objective
3
Need for Timing-Pulse Measurement
• Data collected is only useful if there is synchronization between the
motor- and detector-timing pulses.
• The motor- and detector timing-pulses have to be well synchronized to
assure correlation between the data collected and the measurement
interval.
Aim
Each detector frame should be accurately related to a motor position.
Solution
Measure time stamps using a common time base to relate a motor
position to a detector frame.
5
Sample Detector Timing-Pulse
Sample Motor Timing-Pulse
Common Time-Base (1/1000 resolution)
0 3 6 9 12 ms
0 2 4 6 8 10 12 ms
1
µs
3000 6000 8000 10000 12000 9000 0 2000 4000 µs
Timing-Pulse Measurement: Analyzing the problem
6
• Requires counters working at clock frequencies of 1 MHz or above.
• High data transfer speed
• Fast event notification
Solution
• The USB-4301 is a low-power USB-2.0-compliant, 16-bit, 5
channel, up-down binary counter, capable of operating at frequencies
as high as 5 MHz can be used in event counting and pulse generating
applications.
Timing-Pulse Measurement: Requirement
7
Setup
• Motor- and detector-timing pulses are assigned to separate modules
• Modules are daisy chained to form 32-bit counters
• Terminal count is achieved in ~72 minutes
8
Flow chart
External Circuitry
• Pulse Shaping Circuit
• Start Pulse
• Synchronization Circuit
• Interrupt Mask
• Combined Circuit
Counter Programming
• Initialization
• Configuration
• Counter Save
• Time Stamp
12
Error Range of Measured Time Periods
• Interrupt signal of 2.22 ± 0.003 ms
• Relative error : 0.13%
13
Detector Calibration: Dead Time
Dead Time
• An event occurs at the detector is converted into an electrical signal
depending on the intensity and duration of the event.
• The time required to collect this charge depends on certain
characteristics (mobility, distance to collection electrodes, etc.) of the
detector itself and on the subsequent electronics.
• Due to the random nature governed by Poisson statistics, there is
always a probability that the detector misses a true event that follows a
recorded event.
• The missed true events are called dead-time losses
16
Need for Dead-Time Correction
The measured non-linear and the expected
linear photon counts for varying tube currents
of one detector element from a sample data set
Operating Parameters:
Tube Voltage : 45 kVp
Tube Current: 0 – 1 mA
Photon accumulation time : 50 ms
Aim:
Correct the photon-count loss
due an error level of less than
0.5% of the maximum
expected photon counts
(0.5% of 72,000) ± 350
counts.
The photon counts-vs.-tube
current response plot is
mathematically modeled and
then linearized.
CountsSlope
Current
17
Detector Calibration: Beam Hardening
Beam Hardening
• X-ray beams used in CT are usually polychromatic
• When the photon beam passes through material, it tends to
preferentially loose its lower energy photons, hardening the beam in the
process.
• Lower-energy x-rays are more prone to attenuation, and the average
energy of a polychromatic beam varies with increasing thickness of the
material, thereby making the beam harder.
18
Beam Hardening
Aim:
Correct the non-linearity of the
projection values due to beam
hardening to an error level of
less than 1% of the expected
maximum projection value (1%
of 5 projection value units) ±
0.05.
The projections-vs.-thickness
plot is mathematically modeled
and then linearized. The measured non-linear and
expected linear projection values for
varying absorber thicknesses.
Operating Parameters:
Tube Voltage : 45 kVp
Tube Current: 1 mA
Photon accumulation time : 50 ms
Pr ojectionSlope
Thickness
19
Experimental Setup
• Source : The tube can operate at a maximum anode voltage of 50 kVp
and a maximum anode current of 1 mA, at a maximum operating
temperature of 55oC.
• Detector : The detector is a CZT semi-conductor cuboid of 64 pixilated
elements composed of 50% tellurium, 5% zinc and 45% cadmium.
• Slabs : Slabs are used in the beam hardening experiment as a substitute
for the bone and soft-tissue in human-body (aluminum and Plexiglas). A
total on 19 pairs of these slabs were used.
• Data was collected on 22 dates over a span of nine months.
20
Dead-Time Correction: Steps
1. Modeling using the fourth-degree polynomial function
2. Linearization of the model
3. Drift and stability analysis of the correctioni. Same-date Correction
ii. Different-date Correction
21
Stability of the Dead-Time Correction
• Fit-coefficient vectors were collected
• Corrections applied to the data collected at the same date (same-date
corrections) and a different-date (different-date corrections).
• The stability was analyzed by comparing the residuals
• The corrections were declared stable if their residuals < 350.
• The least expected residuals are those from the same-date corrections
23
Beam-Hardening Correction: Steps
1. Fifth-Degree Polynomial Modeli. Modeling using the polynomial function for 10- and 19-plate data sets
ii. Linearizing the mathematical model
iii. Corrections applied on the 10- and 19-plate data sets
2. Bimodal-Energy Modeli. Modeling using the bimodal-energy model for 10- and 19-plate data sets
ii. Linearizing the mathematical model
iii. Corrections applied on the10- and 19-plate data sets
3. Compare the stability analysis between both models
24
Beam-Hardening Correction
i : 1, 2, 3, ... 19 for the number of slab pairs used
I0 : counts collected with no object in the beam path
Ii : counts collected with i number of slab pairs
µeff : linear attenuation coefficient for Al and Pl
di : thickness of i number of slab pairs
The projection values are generally
linearized to a linear line.
According to Beer’s Law, the projection values of the x-ray beam passing
through an object are linearly proportional to μ(E).
25
Linearization Using the Polynomial Model
• Based on the projection value-vs.-slab thickness plots, it was decided that
an 5th-degree polynomial fit can model these data.
• Each detector element’s data was fitted using a second to a sixth-degree
polynomial function.
26
Bimodal-Energy Model
• The bimodal energy model* suggests that the attenuation is a function
of predominantly two energies, a dominant energy (E2) and a lower
energy (E1).
• The projection values can be modeled using μ1, μ2 and α.
• μ2 is the slope by E2 for large thicknesses
• μ1 is the slope by E1 for smaller thicknesses.
• To solve for the unknowns, the non-linear least squares method is
used.
• The equation system was iteratively solved using a Matlab script by
assuming initial values for the unknown fitting parameters.Ref: de Casteele, E. V., Dyck, D. V., Sijbers, J., and Raman, E. 2002. An energy-based beam hardening model
in tomography. Phys Med Biol 47, 23–30.27
Bimodal-Energy Model
Linear attenuation coefficient (μ(E)) vs. energy for the
Al/Pl slabs.
• The slab pairs were treated as a
homogenous material by calculating
the thickness ratio for a slab pair.
• Energies E2 and E1 are not
predetermined.
• Estimate of the expected lower and
upper bound for μ1 and μ2.
• E2 proved to be greater than E1
28
Linearization Using the Bimodal-Energy Model
• The corrected projection values were obtained by solving till
convergence, with an acceptable error < 0.01 (1%).
• Linearization using both models satisfy the required error criterion
• The stability of the beam-hardening corrections were analyzed by
evaluating the error statistics of the same-date and different-date
corrected values.
29
Secondary Correction
• Primary correction every day is a tedious process.
• Apply primary corrections from one particular date to the data sets
collected from other dates and following this with a secondary correction
(3rd degree polynomial) based only on a few plates (0, 6, 14, 19 or
0, 3, 7, 9) measured on the specific date.
Without Secondary Correction With Secondary Correction 30
Stability analysis for beam-hardening corrections
• Same-date and different-date corrections.– Same-date primary
– Different-date primary
– Different-date-primary followed by secondary
• Data collected on 22 dates, during nine months.
• 134 coefficient matrices for the 10-plate data sets.
• 5 coefficient matrices for the 19-plate data sets.
• Stability for the correction method is assumed if the residuals of the
same-date and different-date corrections are less than 0.05.
31
Results: Dead-Time Correction
Linearization using the fourth-degree model for a data set. Histogram of the individual residuals using
a fourth-degree polynomial correction for a data set
32
Same-Date Corrections: 10 plate data-set
33Corrected projection values and their histograms for the polynomial and
the bimodal-energy model
Different-date corrections: 10 plate data-set
Corrected projection values and their histograms for the polynomial and the
bimodal-energy model
34
Different-date primary followed by secondary correction:
10 plate data-set
35Corrected projection values and their histograms for the polynomial and
the bimodal-energy model
Summary: Correction Methods
Summary of the same-date and different-date primary (Prim) corrections using the fifth degree
polynomial and bimodal-energy models, and the same-date and different-date primary
corrections using both models followed by the secondary (Sec) corrections. The checked cells
represent the methods that produced residuals lower than 0.05.
36
Detector Calibration: Summary
• The same-date dead-time corrections were all within the expected
residual value.
• The data collection required for the dead-time corrections can be
automated.
• Same-date primary corrections consistently produced corrected projection
values that were well within the expected residual of 0.05.
• Most of the residuals for the different-date bimodal corrections were
below 0.05, whereas the residual values for the different-date polynomial
corrections were above 0.05.
Future Work
• Using the non-paralyzable dead-time model.
• Beam hardening corrections should be studied with different tube
voltages.
• Stability of the corrections over a shorter time period can be studied
37
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